Risk measurement for investment using Tail Variance Premium and Tail Standard Deviation premium

Abstract

Information related to the tail of loss distribution especially its variability is vital since tail of distribution is related to big losses and overall risk. Risk measure that is commonly used is Tail Conditional Expectation (TCE) that measures expectation of loss that possibly occur given loss exceeded certain percentiles. However, TCE could not describe clearly the behavior and variability of loss along its tail since it only provides measure of central tendency. Additional information is needed to describe variability of loss, for instance measure of dispersion. In this paper will be discussed further about risk and variability measurement named Tail Variance Premium (TVP) and Tail Standard Deviation Premium (TSDP). They are combination of both central tendency and dispersion statistics, so they can measure variability of loss along the right tail better. TVP and TSDP could be alternative risk measure, especially when risk that is bigger than a certain threshold is concerned. Besides, we will also discuss the criteria satisfied by both risk measures with the proof for each criterion. Next, we also provide the explicit formula of TVP and TSDP for loss with normal distribution in particular. Then we will perform calculation for risk measurement of a stock, both by parametric and non-parametric method. We also show the comparison of risk measurement generated by Value-at-Risk, TCE, TVP, and TSDP.